The ring of integers modulo a prime number has no zero divisors other than 0. Since every nonzero element is a unit, this ring is a finite field. More generally, a division ring has no zero divisors except 0. A nonzero commutative ring whose only zero divisor is 0 is called an integral domain.

How do you prove something has no zero divisors?

The rings Q, R, C are fields. If a, b are elements of a field with ab = 0 then if a ≠ 0 it has an inverse a^-1 and so multiplying both sides by this gives b = 0. Hence there are no zero-divisors and we have: Every field is an integral domain.

Does zero have any divisors?

2 Answers. George C. All non-zero numbers are divisors of 0 . 0 may also be counted as divisor, depending on whose definition of divisor you use.